Question

In Young’s double slit experiment, the slits are 2 mm apart and are illuminated with a mixture of two wavelength λ₀ = 750 nm and λ = 900 nm. What is the minimum distance from the common central bright fringe on a screen 2 m from the slits where a bright fringe from one interference pattern coincides with a bright fringe from the other?

Answer 1

Let n₁ bright fringe of λ₁ coincides with (n+1) bright fringe of λ₂.

`("n"lambda_1"D")/"d" = (("n + 1")lambda_2"D")/"d"`

n × 900 × 10^-9 = (n + 1) × 750 ×10^-9

minimum distance from central maxima = `("n"lambda_1"D")/"d"`

`= (5 xx 900 xx 10^-9 x 2)/(2 xx 10^-3)`

= 4.5 mm